I have posted a very interesting video below where Richard Koo is essentially explaining the process of deleveraging and how to avoid debt deflation. He also explains how Japan narrowly avoided a debt deflationary disaster in the 1990s during the lost decade.

Koo makes the point that Japan and now the US are not in an inventory recession or a recession caused by a central bank trying to control inflation by monetary tightening where the underlying economy is strong: this is a balance sheet recession with excessive private debt, falling asset prices, and deleveraging.
Japan in the 1990s was prevented from a catastrophic depression and the full effects of debt deflation (e.g., the type of collapse in the US from 1929-1933) by stop-and-go use of fiscal policy: but the effectiveness of that fiscal policy was undercut by fiscal conservatives who demanded austerity and budget balancing during the lost decade, most notably in 1997-1998.

In a balance sheet recession, where deleveraging is going on, households are paying down debt and reducing consumption, and business are also repaying debt and reducing gross investment.

This means that private consumption and gross investment collapse in GDP, causing a failure of aggregate demand. Unless you can massively increase exports to make up for this (impossible for most countries), then government spending must step in to fill the shortfall. But for Keynesian stimulus to work effectively, excessive and unsustainable private debt must be written off or restructured and the financial system must be cleared of bad assets and non-performing loans. In Japan, and now as we see in the US and other nations, deleveraging and the poor state of private balance sheets can cause the malaise to go on for years.

Without these measures and additional, larger fiscal stimulus, the US and possibly the UK will most likely experience a lost decade in the 2010s, and now Joseph Stiglitz thinks that the European Union itself will be in for a “lost half-decade” too. Whether the US and European nations will slip into outright deflation again as austerity is implemented is difficult to know. Possibly high energy and commodity prices will keep inflation moderate to high in coming years.

But if serious austerity takes hold in the US a lost decade for America, with a double dip recession, is a real concern. The US may well be the new Japan, so it seems.

Finally, there is further analysis of these issues here from the perspective of MMT:

So would that be a case for one government promoting a stimulus package for a foreign region, in order to boost exports? Perhaps US government and businesses giving massive loans in Mexico, in order that there be a surge in American exports to Mexico?

I suspect such was the motive behind the Indian government putting hundreds of millions of dollars as foreign aid to African countries such as Malawi - to promote its own exports. Recently, there has been a confounding trend for governments in poor countries to send aid and loans to governments in other poor countries.

"So would that be a case for one government promoting a stimulus package for a foreign region,"

Not really. I don't think the Chinese had Germany in mind when they did their huge stimulus - it is just a fact of life that countries that are close trade partners benefit from each other's Keynesian stimulus.

Another reason why it works well when done in countries with close trade ties.

So would that be a case for one government promoting a stimulus package for a foreign region The way Abba Lerner put this thought was that because depressions are contagious, every nation has an international duty to practice functional finance and avoid them. So China is doing its international duty, benefitting Germany, Australia etc, while the US is slacking off.